CBS News national correspondent Hattie Kauffman spoke with "Inside Edition" 's Jim Moret, who said there's talk that Janet has bonded with the children since their father's death.
"She has said, 'I'll step forward and I will raise them if this is what they want," ' Moret said.
Jackson's kids, Michael Joseph Jackson Jr., known as Prince, Paris Michael Katherine Jackson, and Prince Michael Jackson II, known as Blanket, are staying at the Jacskon family home in Encino, Calif., with Michael's mother, Katherine Jackson, as called for in Michael's will.
On "The Early Show" Friday, Kauffman observed that the children's lives are apparently different -- they haven't been seen once with the black face masks they wore while Michael was alive.
Moret said he's talked to a family friend of the Jacksons who said the children are all grieving, but are happy because they're with their relatives.
Kauffman, who toured the Jackson home in 2004, noted the kids can play in the backyard or spend time in its theater.
This week, Kauffman reported, the Jackson children also attended a Jehovah's Witness service with the family.
Firpo Carr, Michael's friend, said the kids are familiar with the tenets of the faith.
"They believe that they're going to see Dad again when he's awakened from his sleep, that is, when he is resurrected from the dead."
A custody hearing for the Jackson children is scheduled for Monday.